{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"3.2线性回归的从零开始实现.ipynb","provenance":[],"collapsed_sections":[]},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"cell_type":"markdown","metadata":{"id":"ID8Y1VfE1iWU","colab_type":"text"},"source":["##3.2 线性回归的从零开始实现\n","&emsp;&emsp;在了解线性回归的背景知识后，现在我们来动手实现它。尽管强大的深度学习框架可以减少大量重复性工作，但过于依赖它提供的便利性，会导致我们很难深入理解深度学习是如何工作的。因此，本节介绍如何利用GradientTape() API来实现一个线性回归的训练。\\\n","&emsp;&emsp;首先，导入本节实验中所需的包或模块，其中的matplotlib包可用于作图，且设置成嵌入显示。\n"]},{"cell_type":"code","metadata":{"id":"ruaoxZgHzXZR","colab_type":"code","colab":{"base_uri":"https://localhost:8080/","height":64},"outputId":"88c97e8b-996c-4dce-82b9-34fe14ff25f3","executionInfo":{"status":"ok","timestamp":1574673799870,"user_tz":-480,"elapsed":3892,"user":{"displayName":"程波","photoUrl":"","userId":"08277046305423172038"}}},"source":["%matplotlib inline\n","from IPython import display\n","from matplotlib import pyplot as pyplot\n","import tensorflow as tf\n","import random\n","import numpy as np\n","\n","tf.enable_eager_execution() #启用动态图计算"],"execution_count":1,"outputs":[{"output_type":"display_data","data":{"text/html":["<p style=\"color: red;\">\n","The default version of TensorFlow in Colab will soon switch to TensorFlow 2.x.<br>\n","We recommend you <a href=\"https://www.tensorflow.org/guide/migrate\" target=\"_blank\">upgrade</a> now \n","or ensure your notebook will continue to use TensorFlow 1.x via the <code>%tensorflow_version 1.x</code> magic:\n","<a href=\"https://colab.research.google.com/notebooks/tensorflow_version.ipynb\" target=\"_blank\">more info</a>.</p>\n"],"text/plain":["<IPython.core.display.HTML object>"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"Wb2JQtC38NIA","colab_type":"text"},"source":["### 3.2.1 生成数据集\n","&emsp;&emsp;我们构造一个简单的人工训练数据集，它可以使我们能够直观比较学习到的参数和真实的模型参数的区别。设训练数据集样本数为1000，输入个数（特征数）为2.给定随机生成的批量样本特征$X \\in R^{1000 \\times2}$,我们使用线性回归模型的真实权重$w=[2,-3,4]^T$和偏差b=4.2，以及一个随机噪声$\\epsilon$来生成标签\n","$$y=Xw+b+\\epsilon ,$$\n","&emsp;&emsp;其中噪声项$\\epsilon$服从均值为0、标准差为0.01的正态分布。噪声代表了数据集中无意义的干扰。下面，让我们生成数据集。"]},{"cell_type":"code","metadata":{"id":"64vox9wi4s8e","colab_type":"code","colab":{}},"source":["num_inputs=2\n","num_examples=1000\n","true_w=[2,-3.4]\n","true_b=4.2\n","features=tf.random.normal(shape=(num_examples,num_inputs),stddev=1)\n","labels=true_w[0]*features[:,0]+true_w[1]*features[:,1]+true_b\n","labels+=tf.random.normal(shape=(tf.shape(labels)),stddev=0.01)"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"cczCwbt927I2","colab_type":"text"},"source":["&emsp;&emsp;注意，features的每一行是一个长度为2的向量，而labels的每一行是一个长度为1的向量(标量)。"]},{"cell_type":"code","metadata":{"id":"WwV1iGdB6Cbf","colab_type":"code","outputId":"84802f51-9853-4c8c-c3f2-49c03d179630","executionInfo":{"status":"ok","timestamp":1574673830137,"user_tz":-480,"elapsed":3196,"user":{"displayName":"程波","photoUrl":"","userId":"08277046305423172038"}},"colab":{"base_uri":"https://localhost:8080/","height":35}},"source":["features.shape,labels.shape"],"execution_count":3,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(TensorShape([Dimension(1000), Dimension(2)]), TensorShape([Dimension(1000)]))"]},"metadata":{"tags":[]},"execution_count":3}]},{"cell_type":"code","metadata":{"id":"qkb136SD6Fsu","colab_type":"code","outputId":"d0e48edb-ad65-4b49-c870-5a8cddd2ffc8","executionInfo":{"status":"ok","timestamp":1574673832021,"user_tz":-480,"elapsed":1180,"user":{"displayName":"程波","photoUrl":"","userId":"08277046305423172038"}},"colab":{"base_uri":"https://localhost:8080/","height":35}},"source":["features[0].numpy(),labels[0].numpy()"],"execution_count":4,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(array([1.2928032 , 0.15362471], dtype=float32), 6.266954)"]},"metadata":{"tags":[]},"execution_count":4}]},{"cell_type":"markdown","metadata":{"id":"svZ3zzXn3OzP","colab_type":"text"},"source":["&emsp;&emsp;通过生成第二个特征features[:,1]和标签labels的散点图，可以更加直观地观察两者间的线性关系。"]},{"cell_type":"code","metadata":{"id":"toWVvEta6SAO","colab_type":"code","colab":{}},"source":["def use_svg_display():\n","  #用矢量图显示\n","  display.set_matplotlib_formats('svg')\n","def set_figsize(figsize=(3.5,2.5)):\n","  use_svg_display()\n","  #设置图的尺寸\n","  pyplot.rcParams['figure.figsize']=figsize"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"jbd_0BZQ6uyX","colab_type":"code","outputId":"fe88e52d-4c38-40dc-ce36-c0d28d6ddb82","executionInfo":{"status":"ok","timestamp":1574673840387,"user_tz":-480,"elapsed":1371,"user":{"displayName":"程波","photoUrl":"","userId":"08277046305423172038"}},"colab":{"base_uri":"https://localhost:8080/","height":261}},"source":["set_figsize()\n","pyplot.scatter(features[:,1].numpy(),labels.numpy(),1)"],"execution_count":6,"outputs":[{"output_type":"execute_result","data":{"text/plain":["<matplotlib.collections.PathCollection at 0x7f57a5b00780>"]},"metadata":{"tags":[]},"execution_count":6},{"output_type":"display_data","data":{"text/plain":["<Figure size 252x180 with 1 Axes>"],"image/svg+xml":"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE 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读取数据\n","&emsp;&emsp;在训练模型的时候，我们需要遍历数据集并不断读取小批量数据样本。这里定义一个函数：它每次返回batch_size（批量大小）个随机样本的特征和标签。"]},{"cell_type":"code","metadata":{"id":"q8Ok1hHY69HB","colab_type":"code","colab":{}},"source":["def data_iter(batch_size,features,labels):\n","  num_examples=len(features)\n","  indices=list(range(num_examples))\n","  random.shuffle(indices)\n","  for i in range(0,num_examples,batch_size):\n","    j=np.array(indices[i:min(i+batch_size,num_examples)])\n","    yield tf.gather(features,j),tf.gather(labels,j)"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"s9IgPKlH1Vfi","colab_type":"text"},"source":["&emsp;&emsp;读取第一个小批量数据样本并打印。每个批量的特征形状为(10,2)，分别对应批量大小和输入个数；标签形状为批量大小。"]},{"cell_type":"code","metadata":{"id":"BjkNLlXS8lNn","colab_type":"code","outputId":"f6eb296d-2f7d-4ca1-a7ec-c2417502698a","executionInfo":{"status":"ok","timestamp":1574673850920,"user_tz":-480,"elapsed":951,"user":{"displayName":"程波","photoUrl":"","userId":"08277046305423172038"}},"colab":{"base_uri":"https://localhost:8080/","height":242}},"source":["batch_size=10\n","for X,y in data_iter(batch_size,features,labels):\n","  print(X,y)\n","  break"],"execution_count":8,"outputs":[{"output_type":"stream","text":["tf.Tensor(\n","[[-0.21719383 -1.0593973 ]\n"," [-0.3221357  -0.3451354 ]\n"," [-2.080672    0.2445377 ]\n"," [-0.06064635  0.77870834]\n"," [-0.7390014  -0.74971086]\n"," [ 0.37659824  0.05508694]\n"," [ 0.07542281  1.5092013 ]\n"," [-1.0215837  -0.44589254]\n"," [-1.1662717   0.08145095]\n"," [ 1.7653456  -0.19372146]], shape=(10, 2), dtype=float32) tf.Tensor(\n","[ 7.375232    4.724717   -0.78952575  1.4377736   5.2782164   4.756109\n"," -0.77351546  3.6853657   1.5922009   8.390103  ], shape=(10,), dtype=float32)\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"6025JIL11sXc","colab_type":"text"},"source":["###3.2.3. 初始化模型参数\n","&emsp;&emsp;将权重初始化成均值为0、标准差为0.01的正太随机数，偏差则初始化成0."]},{"cell_type":"code","metadata":{"id":"8uGDXskD8seP","colab_type":"code","colab":{}},"source":["w=tf.Variable(tf.random.normal(shape=(num_inputs,1),mean=0,stddev=0.01))\n","b=tf.Variable(tf.zeros(shape=(1,)))"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"LhNOrjTc_fjg","colab_type":"code","outputId":"b1d0626e-5a2f-44bf-854a-c6b47a80bdc8","executionInfo":{"status":"ok","timestamp":1574673856557,"user_tz":-480,"elapsed":717,"user":{"displayName":"程波","photoUrl":"","userId":"08277046305423172038"}},"colab":{"base_uri":"https://localhost:8080/","height":35}},"source":["w.shape,b.shape"],"execution_count":10,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(TensorShape([Dimension(2), Dimension(1)]), TensorShape([Dimension(1)]))"]},"metadata":{"tags":[]},"execution_count":10}]},{"cell_type":"markdown","metadata":{"id":"d4fI8LhN2HFg","colab_type":"text"},"source":["### 3.2.4. 定义模型\n","&emsp;&emsp;下面是线性回归的矢量计算表达式的实现。使用tf.matmul()做矩阵乘法。"]},{"cell_type":"code","metadata":{"id":"m-0HtGJa_hVZ","colab_type":"code","colab":{}},"source":["def linreg(X,w,b):\n","  return tf.matmul(X,w)+b"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"azzGf5kC25T2","colab_type":"text"},"source":["### 3.2.5. 定义损失函数\n","&emsp;&emsp;我们使用上一节描述的平方损失来定义线性回归的损失函数。在实现中，我们需要把真实值y变形成预测值y_hat的形状。以下函数返回的结果也将和y_hat的形状相同。"]},{"cell_type":"code","metadata":{"id":"esGQKHD0_son","colab_type":"code","colab":{}},"source":["def squared_loss(y_hat,y):\n","  return (y_hat-tf.reshape(y,shape=y_hat.shape))**2/2"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"QmQlhNN93wgA","colab_type":"text"},"source":["### 3.2.6. 定义优化算法\n","&emsp;&emsp;以下的sgd函数实现了上一节中介绍的小批量随机梯度下降算法。它通过不断迭代模型参数来优化损失函数。这里自动求梯度模块计算得来的梯度是一个批量样本的梯度和。我们将它除以批量大小来得到平均值。"]},{"cell_type":"code","metadata":{"id":"mzGvHYGuB86M","colab_type":"code","colab":{}},"source":["def sgd(params,loss,t,lr,batch_size):\n","  for param in params:\n","    dl_dp=t.gradient(l,param) #求梯度\n","    param.assign_sub(lr*dl_dp/batch_size) #更新梯度"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"nCax3l_C4KHq","colab_type":"text"},"source":["### 3.2.7.训练模型\n","&emsp;&emsp;在训练中，我们将多次迭代模型参数。在每次迭代中，我们根据当前读取到的小批量数据样本(特征X和y)，通过反向传播计算小批量随机梯度，然后调用优化算法sgd迭代模型参数。由于我们之前设批量大小batch_size为10，每个小批量的损失l的形状为(10, 1)。回忆一下“自动求梯度”一节。由于变量l并不是一个标量，运行t.gradient(l,param)将对l中元素求和得到新的变量，再求该变量有关模型参数的梯度。\n","&emsp;&emsp;在一个迭代周期（epoch）中，我们将完整遍历一遍data_iter函数，并对训练数据集中所有样本都使用一次（假设样本数能够被批量大小整除）。这里的迭代周期个数num_epochs和学习率lr都是超参数，分别设3和0.03。在实践中，大多超参数都需要通过反复试错来不断调节。虽然迭代周期数设得越大模型可能越有效，但是训练时间可能过长。而有关学习率对模型的影响，我们会在后面“优化算法”一章中详细介绍。"]},{"cell_type":"code","metadata":{"id":"MLVH8MvnB9CJ","colab_type":"code","outputId":"261bc156-68ae-47b4-9b9d-468b8ec20cf2","executionInfo":{"status":"ok","timestamp":1574674175104,"user_tz":-480,"elapsed":1949,"user":{"displayName":"程波","photoUrl":"","userId":"08277046305423172038"}},"colab":{"base_uri":"https://localhost:8080/","height":69}},"source":["lr=0.03\n","num_epochs=3\n","net=linreg\n","loss=squared_loss\n","\n","for epoch in range(num_epochs):\n","  for X,y in data_iter(batch_size,features,labels):\n","    with tf.GradientTape(persistent=True) as t:\n","      t.watch([w,b])\n","      l=loss(net(X,w,b),y)\n","    sgd([w,b],l,t,lr,batch_size)\n","  train_l=loss(net(features,w,b),labels)\n","  print('epoch %d,loss %f'%(epoch+1,tf.reduce_mean(train_l).numpy()))\n"],"execution_count":14,"outputs":[{"output_type":"stream","text":["epoch 1,loss 0.045622\n","epoch 2,loss 0.000181\n","epoch 3,loss 0.000047\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"2vLHoDnO5e04","colab_type":"text"},"source":["&emsp;&emsp;比较学习到的参数和真实参数，应该很接近"]},{"cell_type":"code","metadata":{"id":"CdR7S8HasBdT","colab_type":"code","outputId":"da831362-d0b2-478a-9c62-4bd4e5f289ed","executionInfo":{"status":"ok","timestamp":1574674259761,"user_tz":-480,"elapsed":957,"user":{"displayName":"程波","photoUrl":"","userId":"08277046305423172038"}},"colab":{"base_uri":"https://localhost:8080/","height":69}},"source":["true_w,w"],"execution_count":15,"outputs":[{"output_type":"execute_result","data":{"text/plain":["([2, -3.4], <tf.Variable 'Variable:0' shape=(2, 1) dtype=float32, numpy=\n"," array([[ 1.999975 ],\n","        [-3.3994184]], dtype=float32)>)"]},"metadata":{"tags":[]},"execution_count":15}]},{"cell_type":"code","metadata":{"id":"2es7TCTBsJKE","colab_type":"code","outputId":"262f0f48-fdec-4497-88ee-7dbd18bb3f9c","executionInfo":{"status":"ok","timestamp":1574674263578,"user_tz":-480,"elapsed":996,"user":{"displayName":"程波","photoUrl":"","userId":"08277046305423172038"}},"colab":{"base_uri":"https://localhost:8080/","height":52}},"source":["true_b,b"],"execution_count":16,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(4.2,\n"," <tf.Variable 'Variable:0' shape=(1,) dtype=float32, numpy=array([4.1995173], dtype=float32)>)"]},"metadata":{"tags":[]},"execution_count":16}]},{"cell_type":"markdown","metadata":{"id":"7Zmb_vJBAKof","colab_type":"text"},"source":["### 3.2.8小结\n","* 可以看出，仅使用Tensor和GradientTape() API就可以很容易地实现一个模型。接下来会在此基础上描述更多深度学习模型，并介绍怎样使用更简洁地代码(见下一节)来实现它们。\n","  "]},{"cell_type":"code","metadata":{"id":"wq_FlCdV6ufp","colab_type":"code","colab":{}},"source":[""],"execution_count":0,"outputs":[]}]}